An efficient combination between Berlekamp-Massey and Hartmann Rudolph algorithms to decode BCH codes

Abstract

In digital communication and storage systems, the exchange of data is achieved using a communication channel which is not completely reliable. Therefore, detection and correction of possible errors are required by adding redundant bits to information data. Several algebraic and heuristic decoders were designed to detect and correct errors. The Hartmann Rudolph (HR) algorithm enables to decode a sequence symbol by symbol. The HR algorithm has a high complexity, that's why we suggest using it partially with the algebraic hard decision decoder Berlekamp-Massey (BM). In this work, we propose a concatenation of Partial Hartmann Rudolph (PHR) algorithm and Berlekamp-Massey decoder to decode BCH (Bose-Chaudhuri-Hocquenghem) codes. Very satisfying results are obtained. For example, we have used only 0.54% of the dual space size for the BCH code (63,39,9) while maintaining very good decoding quality. To judge our results, we compare them with other decoders.

Improved Decoding of Linear Block Codes by Concatenated Decoders

“…a In Fig. 5, we present the performances of our PHR Chase decoder for some quadratic residue (QR) codes of lengths up to 71 and we deduce that the coding gain is about 3,8 dB for QR (23,12,7), 4 dB for QR (31,16,7), 4,8 dB for QR(47, 24, 11) and 5.1 dB for QR (71,36,11). Thus, we deduce that the correction performances improve with the length of the code, for example the QR(71, 36, 11) code guarantees a coding gain of 1,3 dB comparing to QR (23,12,7) code.…”

“…Recently, we find several decoding algorithms that are defined by concatenating two serial decoders [16,33,35,36]. In [16], the authors proposed to use the HR algorithm partially with a reduced number of dual code words and correct just symbols whose reliability is below a threshold, then to use a second decoder to complete the decoding of the recovered sequence at the output of the HR decoder.…”

“…Several works use hashing techniques to speed up the decoding process and therefore have reduced complexity in execution time [30]- [35]. There are also decoders developed by serial concatenation of two decoders [16,34,35,36].…”

Machine learning for decoding linear block codes: case of multi-class logistic regression model

“…There are other methods that use non-algebraic techniques, such as genetic algorithms that belong to evolutionary techniques [18]- [19]. We have also found a work that uses local search to find errors [20]- [21]. Moreover, several other works use hashing techniques [22]- [23].…”